Note the resemblance to the ideal gas law! Note also how the dotted line in Figure
22.11 mimics the hyperbolic curve of an inverse relationship between and A,
that is, Boyle’s law. In these regions, each molecule can wiggle around indepen-
dently of the others, and can be modeled as a sort of two-dimensional gas.
In regions where each molecule covers an area approximately equal to its
own area, is relatively constant. The size of these regions is highly dependent
on the molecule making up the film. However, if the film is compressed be-
yond a certain point, the surface pressure increases dramatically, as shown on
the left side of Figure 22.11. In these regions the surface film is forced into a
multimolecular film, instead of a monomolecular film. The surface pressure
thus represents the surface energy needed to force layers of molecules over each
other.
Surface films are very common, although they may be easily overlooked. Oil
on water has already been mentioned as a type of surface film. One very im-
portant surface film is a cell membrane. As seen in Figure 22.12, cell mem-
branes are films of lipids that exist on the surfaces of protoplasm. The physi-
cal and chemical properties of these films are crucial to the ability of the cells
to maintain a living state.22.5 Solid Surfaces
All solids terminate their structure at some point. This termination is the sur-
face of the solid. Consider the surface of any object near you right now (this
page, for example). At the level of human perception, there seems nothing
strange or unusual about the surface of the solid object.
Partly, that’s because solid surfaces are so familiar to us. We don’t bother to
question whether they have any interesting or unique characteristics. Actually,
many solids don’thave interesting or unique characteristics. Any random ob-
ject has a rather messy surface at the atomic or molecular level. (See Figure
22.13 for a close-up of a surface.) They are multi- or polycrystalline or even
amorphous, yielding a random surface that is so complicated, so random, that
there is very little to be ableto understand about its behavior.
Therefore, in physical chemistry we require that the surfaces we study be a
little more regular, a little more ordered. If we want to model a solid surface,
that surface should be described by a relatively simple structure. It should not
be a polycrystalline, random collection of solid particles. Model surfaces should
be simple, regular, and easy to define.
We actually described planes of atoms in Chapter 21. We used Miller indices
to define planes of atoms in a solid crystal. A proper model surface should be
a simple plane of atoms, so we suggest that any good model surface should be
described by the Miller indices of the plane to which the surface atoms belong.
Figure 22.14 shows our point. First, Figure 22.14a shows Miller index planes
inside a solid crystal. The designation (110) is consistent with our under-778 CHAPTER 22 SurfacesFigure 22.12 In biological cells, the cell mem-
brane is a film. The ability of the cell to function,
or live, is highly dependent on the ability of the
cell membrane to work properly.Figure 22.13 Any random surface is actually
very messy at the atomic level. This picture shows
the surface of “smooth” stainless steele, magnified
10,000 times.(110)
Planes(a)(110)
Surface(b)Figure 22.14 (a) Planes of atoms in a crystal
are defined by Miller indices. (b) An exposed sur-
face plane of atoms can also be described using
the same Miller indices.© 1999 Michael Dalton, FundamentalPhotographs, NYC
© Bruce Iverson/Iverson Science Photos